Softneck is the one that will store a long time. They have lots of smaller cloves instead of a few large ones (hardnecks are the ones with just a few large cloves). Hardnecks don't store as long and are meant to be eaten within a few months at most.
Softneck does not produce a garlic scape or flower, hardnecks do and the flowers will turn into bulbils if you let them go. These can be replanted but it takes a few years for them to become real garlic.
I like to do a mix of both because we like to eat the garlic scapes, too.
Hardnecks are generally considered spicier than softnecks as well but I haven't always found that to be true.
This month's Herb Companion is all about garlic. It looks like most of the info is online here: http://www.herbcompanion.com/cooking/garlic-makes-it-good.aspx
I think Seeds of Change has a good selection of organic planting garlic but Filaree Farms seems to be the one with a real selection. Filaree also has lots of garlic info that helps you figure out what you should plant.